Polytope of Type {9,12,4}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,12,4}*1728
if this polytope has a name.
Group : SmallGroup(1728,30313)
Rank : 4
Schlafli Type : {9,12,4}
Number of vertices, edges, etc : 18, 108, 48, 4
Order of s0s1s2s3 : 36
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {9,12,2}*864
3-fold quotients : {9,4,4}*576b, {3,12,4}*576
4-fold quotients : {9,6,4}*432
6-fold quotients : {9,4,2}*288, {3,12,2}*288
8-fold quotients : {9,6,2}*216
9-fold quotients : {3,4,4}*192b
12-fold quotients : {9,2,4}*144, {9,4,2}*144, {3,6,4}*144
18-fold quotients : {3,4,2}*96
24-fold quotients : {9,2,2}*72, {3,6,2}*72
36-fold quotients : {3,2,4}*48, {3,4,2}*48
72-fold quotients : {3,2,2}*24
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 25)( 14, 26)( 15, 28)
( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)
( 24, 31)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)
( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49,105)( 50,106)( 51,108)
( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)( 59,100)
( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)( 67, 92)
( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)(111,112)(113,117)(114,118)
(115,120)(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)
(127,144)(128,143)(129,137)(130,138)(131,140)(132,139)(145,189)(146,190)
(147,192)(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)(154,182)
(155,184)(156,183)(157,213)(158,214)(159,216)(160,215)(161,209)(162,210)
(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)(170,202)
(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)(178,194)
(179,196)(180,195)(219,220)(221,225)(222,226)(223,228)(224,227)(229,241)
(230,242)(231,244)(232,243)(233,249)(234,250)(235,252)(236,251)(237,245)
(238,246)(239,248)(240,247)(253,297)(254,298)(255,300)(256,299)(257,293)
(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)(264,291)(265,321)
(266,322)(267,324)(268,323)(269,317)(270,318)(271,320)(272,319)(273,313)
(274,314)(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)(281,305)
(282,306)(283,308)(284,307)(285,301)(286,302)(287,304)(288,303)(327,328)
(329,333)(330,334)(331,336)(332,335)(337,349)(338,350)(339,352)(340,351)
(341,357)(342,358)(343,360)(344,359)(345,353)(346,354)(347,356)(348,355)
(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)(368,403)
(369,397)(370,398)(371,400)(372,399)(373,429)(374,430)(375,432)(376,431)
(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)(384,423)
(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)(392,415)
(393,409)(394,410)(395,412)(396,411);;
s1 := ( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 57)( 6, 60)( 7, 59)( 8, 58)
( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 37)( 14, 40)( 15, 39)( 16, 38)
( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 41)( 22, 44)( 23, 43)( 24, 42)
( 25, 61)( 26, 64)( 27, 63)( 28, 62)( 29, 69)( 30, 72)( 31, 71)( 32, 70)
( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 73, 93)( 74, 96)( 75, 95)( 76, 94)
( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 85)( 82, 88)( 83, 87)( 84, 86)
( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,157)(110,160)(111,159)
(112,158)(113,165)(114,168)(115,167)(116,166)(117,161)(118,164)(119,163)
(120,162)(121,145)(122,148)(123,147)(124,146)(125,153)(126,156)(127,155)
(128,154)(129,149)(130,152)(131,151)(132,150)(133,169)(134,172)(135,171)
(136,170)(137,177)(138,180)(139,179)(140,178)(141,173)(142,176)(143,175)
(144,174)(181,201)(182,204)(183,203)(184,202)(185,197)(186,200)(187,199)
(188,198)(189,193)(190,196)(191,195)(192,194)(205,213)(206,216)(207,215)
(208,214)(210,212)(217,265)(218,268)(219,267)(220,266)(221,273)(222,276)
(223,275)(224,274)(225,269)(226,272)(227,271)(228,270)(229,253)(230,256)
(231,255)(232,254)(233,261)(234,264)(235,263)(236,262)(237,257)(238,260)
(239,259)(240,258)(241,277)(242,280)(243,279)(244,278)(245,285)(246,288)
(247,287)(248,286)(249,281)(250,284)(251,283)(252,282)(289,309)(290,312)
(291,311)(292,310)(293,305)(294,308)(295,307)(296,306)(297,301)(298,304)
(299,303)(300,302)(313,321)(314,324)(315,323)(316,322)(318,320)(325,373)
(326,376)(327,375)(328,374)(329,381)(330,384)(331,383)(332,382)(333,377)
(334,380)(335,379)(336,378)(337,361)(338,364)(339,363)(340,362)(341,369)
(342,372)(343,371)(344,370)(345,365)(346,368)(347,367)(348,366)(349,385)
(350,388)(351,387)(352,386)(353,393)(354,396)(355,395)(356,394)(357,389)
(358,392)(359,391)(360,390)(397,417)(398,420)(399,419)(400,418)(401,413)
(402,416)(403,415)(404,414)(405,409)(406,412)(407,411)(408,410)(421,429)
(422,432)(423,431)(424,430)(426,428);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 26)( 14, 25)
( 15, 28)( 16, 27)( 17, 30)( 18, 29)( 19, 32)( 20, 31)( 21, 34)( 22, 33)
( 23, 36)( 24, 35)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)
( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 66)( 54, 65)( 55, 68)( 56, 67)
( 57, 70)( 58, 69)( 59, 72)( 60, 71)( 73, 74)( 75, 76)( 77, 78)( 79, 80)
( 81, 82)( 83, 84)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89,102)( 90,101)
( 91,104)( 92,103)( 93,106)( 94,105)( 95,108)( 96,107)(109,110)(111,112)
(113,114)(115,116)(117,118)(119,120)(121,134)(122,133)(123,136)(124,135)
(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)(132,143)
(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,170)(158,169)
(159,172)(160,171)(161,174)(162,173)(163,176)(164,175)(165,178)(166,177)
(167,180)(168,179)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)
(193,206)(194,205)(195,208)(196,207)(197,210)(198,209)(199,212)(200,211)
(201,214)(202,213)(203,216)(204,215)(217,326)(218,325)(219,328)(220,327)
(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)(228,335)
(229,350)(230,349)(231,352)(232,351)(233,354)(234,353)(235,356)(236,355)
(237,358)(238,357)(239,360)(240,359)(241,338)(242,337)(243,340)(244,339)
(245,342)(246,341)(247,344)(248,343)(249,346)(250,345)(251,348)(252,347)
(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)(260,367)
(261,370)(262,369)(263,372)(264,371)(265,386)(266,385)(267,388)(268,387)
(269,390)(270,389)(271,392)(272,391)(273,394)(274,393)(275,396)(276,395)
(277,374)(278,373)(279,376)(280,375)(281,378)(282,377)(283,380)(284,379)
(285,382)(286,381)(287,384)(288,383)(289,398)(290,397)(291,400)(292,399)
(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)(300,407)
(301,422)(302,421)(303,424)(304,423)(305,426)(306,425)(307,428)(308,427)
(309,430)(310,429)(311,432)(312,431)(313,410)(314,409)(315,412)(316,411)
(317,414)(318,413)(319,416)(320,415)(321,418)(322,417)(323,420)(324,419);;
s3 := ( 1,217)( 2,218)( 3,219)( 4,220)( 5,221)( 6,222)( 7,223)( 8,224)
( 9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)( 16,232)
( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)( 24,240)
( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)( 32,248)
( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)( 40,256)
( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)( 48,264)
( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)( 56,272)
( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)( 64,280)
( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)( 72,288)
( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)( 80,296)
( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)( 88,304)
( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)( 96,312)
( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)(104,320)
(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)(112,328)
(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)(120,336)
(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)(128,344)
(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)(136,352)
(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)(144,360)
(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)(152,368)
(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)(160,376)
(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)(168,384)
(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)(176,392)
(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)(184,400)
(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)(192,408)
(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)(200,416)
(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)(208,424)
(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)(216,432);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(432)!( 3, 4)( 5, 9)( 6, 10)( 7, 12)( 8, 11)( 13, 25)( 14, 26)
( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)
( 23, 32)( 24, 31)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)
( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49,105)( 50,106)
( 51,108)( 52,107)( 53,101)( 54,102)( 55,104)( 56,103)( 57, 97)( 58, 98)
( 59,100)( 60, 99)( 61, 93)( 62, 94)( 63, 96)( 64, 95)( 65, 89)( 66, 90)
( 67, 92)( 68, 91)( 69, 85)( 70, 86)( 71, 88)( 72, 87)(111,112)(113,117)
(114,118)(115,120)(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)
(126,142)(127,144)(128,143)(129,137)(130,138)(131,140)(132,139)(145,189)
(146,190)(147,192)(148,191)(149,185)(150,186)(151,188)(152,187)(153,181)
(154,182)(155,184)(156,183)(157,213)(158,214)(159,216)(160,215)(161,209)
(162,210)(163,212)(164,211)(165,205)(166,206)(167,208)(168,207)(169,201)
(170,202)(171,204)(172,203)(173,197)(174,198)(175,200)(176,199)(177,193)
(178,194)(179,196)(180,195)(219,220)(221,225)(222,226)(223,228)(224,227)
(229,241)(230,242)(231,244)(232,243)(233,249)(234,250)(235,252)(236,251)
(237,245)(238,246)(239,248)(240,247)(253,297)(254,298)(255,300)(256,299)
(257,293)(258,294)(259,296)(260,295)(261,289)(262,290)(263,292)(264,291)
(265,321)(266,322)(267,324)(268,323)(269,317)(270,318)(271,320)(272,319)
(273,313)(274,314)(275,316)(276,315)(277,309)(278,310)(279,312)(280,311)
(281,305)(282,306)(283,308)(284,307)(285,301)(286,302)(287,304)(288,303)
(327,328)(329,333)(330,334)(331,336)(332,335)(337,349)(338,350)(339,352)
(340,351)(341,357)(342,358)(343,360)(344,359)(345,353)(346,354)(347,356)
(348,355)(361,405)(362,406)(363,408)(364,407)(365,401)(366,402)(367,404)
(368,403)(369,397)(370,398)(371,400)(372,399)(373,429)(374,430)(375,432)
(376,431)(377,425)(378,426)(379,428)(380,427)(381,421)(382,422)(383,424)
(384,423)(385,417)(386,418)(387,420)(388,419)(389,413)(390,414)(391,416)
(392,415)(393,409)(394,410)(395,412)(396,411);
s1 := Sym(432)!( 1, 49)( 2, 52)( 3, 51)( 4, 50)( 5, 57)( 6, 60)( 7, 59)
( 8, 58)( 9, 53)( 10, 56)( 11, 55)( 12, 54)( 13, 37)( 14, 40)( 15, 39)
( 16, 38)( 17, 45)( 18, 48)( 19, 47)( 20, 46)( 21, 41)( 22, 44)( 23, 43)
( 24, 42)( 25, 61)( 26, 64)( 27, 63)( 28, 62)( 29, 69)( 30, 72)( 31, 71)
( 32, 70)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 73, 93)( 74, 96)( 75, 95)
( 76, 94)( 77, 89)( 78, 92)( 79, 91)( 80, 90)( 81, 85)( 82, 88)( 83, 87)
( 84, 86)( 97,105)( 98,108)( 99,107)(100,106)(102,104)(109,157)(110,160)
(111,159)(112,158)(113,165)(114,168)(115,167)(116,166)(117,161)(118,164)
(119,163)(120,162)(121,145)(122,148)(123,147)(124,146)(125,153)(126,156)
(127,155)(128,154)(129,149)(130,152)(131,151)(132,150)(133,169)(134,172)
(135,171)(136,170)(137,177)(138,180)(139,179)(140,178)(141,173)(142,176)
(143,175)(144,174)(181,201)(182,204)(183,203)(184,202)(185,197)(186,200)
(187,199)(188,198)(189,193)(190,196)(191,195)(192,194)(205,213)(206,216)
(207,215)(208,214)(210,212)(217,265)(218,268)(219,267)(220,266)(221,273)
(222,276)(223,275)(224,274)(225,269)(226,272)(227,271)(228,270)(229,253)
(230,256)(231,255)(232,254)(233,261)(234,264)(235,263)(236,262)(237,257)
(238,260)(239,259)(240,258)(241,277)(242,280)(243,279)(244,278)(245,285)
(246,288)(247,287)(248,286)(249,281)(250,284)(251,283)(252,282)(289,309)
(290,312)(291,311)(292,310)(293,305)(294,308)(295,307)(296,306)(297,301)
(298,304)(299,303)(300,302)(313,321)(314,324)(315,323)(316,322)(318,320)
(325,373)(326,376)(327,375)(328,374)(329,381)(330,384)(331,383)(332,382)
(333,377)(334,380)(335,379)(336,378)(337,361)(338,364)(339,363)(340,362)
(341,369)(342,372)(343,371)(344,370)(345,365)(346,368)(347,367)(348,366)
(349,385)(350,388)(351,387)(352,386)(353,393)(354,396)(355,395)(356,394)
(357,389)(358,392)(359,391)(360,390)(397,417)(398,420)(399,419)(400,418)
(401,413)(402,416)(403,415)(404,414)(405,409)(406,412)(407,411)(408,410)
(421,429)(422,432)(423,431)(424,430)(426,428);
s2 := Sym(432)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9, 10)( 11, 12)( 13, 26)
( 14, 25)( 15, 28)( 16, 27)( 17, 30)( 18, 29)( 19, 32)( 20, 31)( 21, 34)
( 22, 33)( 23, 36)( 24, 35)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)
( 47, 48)( 49, 62)( 50, 61)( 51, 64)( 52, 63)( 53, 66)( 54, 65)( 55, 68)
( 56, 67)( 57, 70)( 58, 69)( 59, 72)( 60, 71)( 73, 74)( 75, 76)( 77, 78)
( 79, 80)( 81, 82)( 83, 84)( 85, 98)( 86, 97)( 87,100)( 88, 99)( 89,102)
( 90,101)( 91,104)( 92,103)( 93,106)( 94,105)( 95,108)( 96,107)(109,110)
(111,112)(113,114)(115,116)(117,118)(119,120)(121,134)(122,133)(123,136)
(124,135)(125,138)(126,137)(127,140)(128,139)(129,142)(130,141)(131,144)
(132,143)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,170)
(158,169)(159,172)(160,171)(161,174)(162,173)(163,176)(164,175)(165,178)
(166,177)(167,180)(168,179)(181,182)(183,184)(185,186)(187,188)(189,190)
(191,192)(193,206)(194,205)(195,208)(196,207)(197,210)(198,209)(199,212)
(200,211)(201,214)(202,213)(203,216)(204,215)(217,326)(218,325)(219,328)
(220,327)(221,330)(222,329)(223,332)(224,331)(225,334)(226,333)(227,336)
(228,335)(229,350)(230,349)(231,352)(232,351)(233,354)(234,353)(235,356)
(236,355)(237,358)(238,357)(239,360)(240,359)(241,338)(242,337)(243,340)
(244,339)(245,342)(246,341)(247,344)(248,343)(249,346)(250,345)(251,348)
(252,347)(253,362)(254,361)(255,364)(256,363)(257,366)(258,365)(259,368)
(260,367)(261,370)(262,369)(263,372)(264,371)(265,386)(266,385)(267,388)
(268,387)(269,390)(270,389)(271,392)(272,391)(273,394)(274,393)(275,396)
(276,395)(277,374)(278,373)(279,376)(280,375)(281,378)(282,377)(283,380)
(284,379)(285,382)(286,381)(287,384)(288,383)(289,398)(290,397)(291,400)
(292,399)(293,402)(294,401)(295,404)(296,403)(297,406)(298,405)(299,408)
(300,407)(301,422)(302,421)(303,424)(304,423)(305,426)(306,425)(307,428)
(308,427)(309,430)(310,429)(311,432)(312,431)(313,410)(314,409)(315,412)
(316,411)(317,414)(318,413)(319,416)(320,415)(321,418)(322,417)(323,420)
(324,419);
s3 := Sym(432)!( 1,217)( 2,218)( 3,219)( 4,220)( 5,221)( 6,222)( 7,223)
( 8,224)( 9,225)( 10,226)( 11,227)( 12,228)( 13,229)( 14,230)( 15,231)
( 16,232)( 17,233)( 18,234)( 19,235)( 20,236)( 21,237)( 22,238)( 23,239)
( 24,240)( 25,241)( 26,242)( 27,243)( 28,244)( 29,245)( 30,246)( 31,247)
( 32,248)( 33,249)( 34,250)( 35,251)( 36,252)( 37,253)( 38,254)( 39,255)
( 40,256)( 41,257)( 42,258)( 43,259)( 44,260)( 45,261)( 46,262)( 47,263)
( 48,264)( 49,265)( 50,266)( 51,267)( 52,268)( 53,269)( 54,270)( 55,271)
( 56,272)( 57,273)( 58,274)( 59,275)( 60,276)( 61,277)( 62,278)( 63,279)
( 64,280)( 65,281)( 66,282)( 67,283)( 68,284)( 69,285)( 70,286)( 71,287)
( 72,288)( 73,289)( 74,290)( 75,291)( 76,292)( 77,293)( 78,294)( 79,295)
( 80,296)( 81,297)( 82,298)( 83,299)( 84,300)( 85,301)( 86,302)( 87,303)
( 88,304)( 89,305)( 90,306)( 91,307)( 92,308)( 93,309)( 94,310)( 95,311)
( 96,312)( 97,313)( 98,314)( 99,315)(100,316)(101,317)(102,318)(103,319)
(104,320)(105,321)(106,322)(107,323)(108,324)(109,325)(110,326)(111,327)
(112,328)(113,329)(114,330)(115,331)(116,332)(117,333)(118,334)(119,335)
(120,336)(121,337)(122,338)(123,339)(124,340)(125,341)(126,342)(127,343)
(128,344)(129,345)(130,346)(131,347)(132,348)(133,349)(134,350)(135,351)
(136,352)(137,353)(138,354)(139,355)(140,356)(141,357)(142,358)(143,359)
(144,360)(145,361)(146,362)(147,363)(148,364)(149,365)(150,366)(151,367)
(152,368)(153,369)(154,370)(155,371)(156,372)(157,373)(158,374)(159,375)
(160,376)(161,377)(162,378)(163,379)(164,380)(165,381)(166,382)(167,383)
(168,384)(169,385)(170,386)(171,387)(172,388)(173,389)(174,390)(175,391)
(176,392)(177,393)(178,394)(179,395)(180,396)(181,397)(182,398)(183,399)
(184,400)(185,401)(186,402)(187,403)(188,404)(189,405)(190,406)(191,407)
(192,408)(193,409)(194,410)(195,411)(196,412)(197,413)(198,414)(199,415)
(200,416)(201,417)(202,418)(203,419)(204,420)(205,421)(206,422)(207,423)
(208,424)(209,425)(210,426)(211,427)(212,428)(213,429)(214,430)(215,431)
(216,432);
poly := sub<Sym(432)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope